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Clustering is a well-studied unsupervised learning task that aims to partition data points into a number of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV…
In this paper, we consider lightweight decentralised algorithms for achieving consensus in distributed systems. Each member of a distributed group has a private value from a fixed set consisting of, say, two elements, and the goal is for…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
Understanding semantic similarity among images is the core of a wide range of computer vision applications. An important step towards this goal is to collect and learn human perceptions. Interestingly, the semantic context of images is…
Consensus clustering aggregates partitions in order to find a better fit by reconciling clustering results from different sources/executions. In practice, there exist noise and outliers in clustering task, which, however, may significantly…
K-means plays a vital role in data mining and is the simplest and most widely used algorithm under the Euclidean Minimum Sum-of-Squares Clustering (MSSC) model. However, its performance drastically drops when applied to vast amounts of…
The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Many applications motivate the distance measure between rankings, such as comparing top-k lists and rank aggregation for voting, and intrigue great interest to researchers. For example, for a search engine, the use of different ranking…
Inverse optimization has received much attention in recent years, but little literature exists for solving generalized mixed integer inverse optimization. We propose a new approach for solving generalized mixed-integer inverse optimization…
Classical work on metric space based committee selection problem interprets distance as ``near is better''. In this work, motivated by real-life situations, we interpret distance as ``far is better''. Formally stated, we initiate the study…
Uncertainty arises naturally inmany application domains due to, e.g., data entry errors and ambiguity in data cleaning. Prior work in incomplete and probabilistic databases has investigated the semantics and efficient evaluation of ranking…
We extend Random Access, a fundamental operation that enables efficient search and exploration algorithms, to the modern interactive data systems based on Ranked Retrieval and Similarity Search, where orderings are dynamically defined over…
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
We present a merge-free algorithm for multi-way co-ranking, the problem of computing cut indices $i_1,\dots,i_m$ that partition each of the $m$ sorted sequences such that all prefix segments together contain exactly $K$ elements. Our method…
The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…
Van Zuylen et al. [35] introduced the notion of a popular ranking in a voting context, where each voter submits a strict ranking of all candidates. A popular ranking $\pi$ of the candidates is at least as good as any other ranking $\sigma$…
A method for aggregation of expert estimates in small groups is proposed. The method is based on combinatorial approach to decomposition of pair-wise comparison matrices and to processing of expert data. It also uses the basic principles of…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact…